How many different proteins, each with a unique amino acid sequence, can be constructed that have a length of five amino acids?

Verified step by step guidance

1. Identify the number of different amino acids available for constructing proteins, which is 20.
2. Understand that each position in the protein sequence can be occupied by any of the 20 amino acids.
3. Recognize that for a protein of length five, each of the five positions can independently be one of the 20 amino acids.
4. Use the rule of multiplication for independent events to calculate the total number of unique sequences: multiply the number of choices for each position.
5. Express the calculation as \( 20^5 \), representing the total number of different proteins with a unique sequence of five amino acids.

Key Concepts

Amino Acids

Amino acids are the building blocks of proteins, consisting of a central carbon atom, an amino group, a carboxyl group, a hydrogen atom, and a variable R group. There are 20 standard amino acids, each with unique properties determined by their R groups. The sequence and composition of these amino acids dictate the structure and function of the resulting protein.

Protein Synthesis

Protein synthesis is the biological process through which cells generate proteins, involving transcription of DNA to mRNA and translation of mRNA to a polypeptide chain. The order of amino acids in the polypeptide is determined by the sequence of nucleotides in the mRNA, which is derived from the DNA template. This process is crucial for producing proteins with specific functions in the organism.

Combinatorial Possibilities

Combinatorial possibilities refer to the different ways in which a set of items can be arranged or combined. In the context of protein construction, if each position in a five-amino-acid sequence can be filled by any of the 20 amino acids, the total number of unique sequences can be calculated using the formula 20^n, where n is the length of the sequence. For a length of five, this results in 20^5 unique combinations.